Answer to Question #119221 in Statistics and Probability for Math

Question

the average Mark of candidates in an aptitude test was 128.5 with a standard deviation of 8 points to the three scores extracted from the test are 148 102 and 152 what is the average of the extractor scores that are extreme values

Answer 1

$\text{According to Z- score }\\ \text{any data value with a z-score less}\\ \text{ than -2 or greater than 2 as an outlier}\\ Z=\frac{x- \mu}{\sigma}\\ Z_{148}=\frac{148- 128.5}{8.2}=2.38\\ Z_{102}=\frac{102- 128.5}{8.2}=-3.23\\ Z_{152}=\frac{152- 128.5}{8.2}=2.86\\ \text{ so all of them are outliers}\\ \text{the average of the extracted scores that }\\ \text{are extreme values (outliers)} \\=\frac{148+102+152}{3}=134$